Prime and Primitive Ideals of Ultragraph Leavitt Path Algebras

A. Pourabbas; M. Imanfar; H. Larki

Prime and Primitive Ideals of Ultragraph Leavitt Path Algebras

Rings and Algebras 2021-09-27 v1 Operator Algebras

Authors: A. Pourabbas , M. Imanfar , H. Larki

Abstract

Let $\mathcal G$ be an ultragraph and let $K$ be a field. We describe prime and primitive ideals in the ultragraph Leavitt path algebra $L_K(\mathcal G)$ . We identify the graded prime ideals in terms of downward directed sets and then we characterize the non-graded prime ideals. We show that the non-graded prime ideals of $L_K(\mathcal G)$ are always primitive.

Keywords

ultragraph leavitt path algebra prime ideals primitive ideals graded ideals downward directed sets

Cite

@article{arxiv.2109.12011,
  title  = {Prime and Primitive Ideals of Ultragraph Leavitt Path Algebras},
  author = {A. Pourabbas and M. Imanfar and H. Larki},
  journal= {arXiv preprint arXiv:2109.12011},
  year   = {2021}
}

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